The fundamental group of reductive Borel-Serre and Satake compactifications

Let $G$ be an almost simple, simply connected algebraic group defined over a number field $k$, and let $S$ be a finite set of places of $k$ including all infinite places. Let $X$ be the product over $v\in S$ of the symmetric spaces associated to $G(k_v)$, when $v$ is an infinite place, and the Bruhat-Tits buildings associated to $G(k_v)$, when $v$ is a finite place. The main result of this paper is an explicit computation of the fundamental group of the reductive Borel-Serre compactification of $\Gamma\backslash X$, where $\Gamma$ is an $S$-arithmetic subgroup of $G$. In the case that $\Gamma$ is neat, we show that this fundamental group is isomorphic to $\Gamma/E\Gamma$, where $E\Gamma$ is the subgroup generated by the elements of $\Gamma$ belonging to unipotent radicals of $k$-parabolic subgroups. Analogous computations of the fundamental group of the Satake compactifications are made. It is noteworthy that calculations of the congruence subgroup kernel $C(S,G)$ yield similar results.Comment: 21 pages, 1 figure, uses Xy-pic 3.8.6; in version 2, title changed to more accurately reflect main result, expository material on congruence subgroup problem removed, many small corrections and improvements in expositio

Effect of Process Variables on High-Tension Separation - A Statistical Approach

The minerals like ilmenite, rutile and leucoxene behave as conducting minerals where as zircon, sillimanite, garnet and monazite behave as non-conducting minerals when high potential difference is applied. In a mineral processing plants effective separation of the conducting minerals depends on the efficiency of electrostatic separators. The commercial equipment are designed in an electro dynamic and electrostatic operating conditions depending on the process requirement and several stages of such operations are necessary to produce high pure mineral products with good recovery. The separation process becomes relatively more dcult when the particle size distribution is in wider ranging from very fine to coarser along with coated non-conducting minerals. The present study deals with the use of high-tension separa-tor in processing heavy minerals for recovery of conducting minerals. The process variables have been optimized with the help of statistical design of exper-iments and co-relations have been developed between the operating variables of high-tension separator, yield and the grade of conducting minerals recovered

Classification of Facial Expressions based on Transitions Derived from Third Order Neighborhood LBP

The present paper extended the LBP transitions derived from second-order neighbourhood on to third order neighbourhood LBP (TN-LBP) and derived transitions on Trapezoid patterns for facial expression classification. The TN-LBP forms four Trapezoid Patterns (TP) i.e. top left, bottom right and top right, bottom left. So far no researcher carried out work on classification problem based on transitions on third-order neighborhood LBP. The present paper derived transitions on the two reciprocal 201C;Trapezoids of TN-LBP (T-TN-LBP) i.e. top left vs. bottom right. Each of these Trapezoids on TN-LBP will have five pixies and each of them will have 25 i.e 32 patterns. The present paper derived transitions on two symmetric T-TN-LBP. Based on this, facial expression recognition algorithm is built. The proposed approach is compared with the existing methods

Steel Industry-Wastes as New Materials for Road Construction

A large number of steel plants have been set up in India and they are producing several million tonnes of iron and steel. However, the production of iron and steel is always associated with the generation of waste materials like air cooled slag, steel slag, granulated slag and flyash etc. These materials are posing serious problems of disposal and causing environmental pollution. Road Construction is one such sector where these materials can be utilised in bulk. CRRI started a few projects sponsored by Steel Authority of India Limited (SAIL), and all these materials were tested on a big scale in CRRI laboratory. Based on the success of laboratory results, various combinations were tried in the field and finally a road was constructed. This road has been monitored regularly for surface unevenness and pavement structural strength. This paper gives the results of extensive laboratory investigations and performance of the road